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Simple shear of a compressible quasilinear viscoelastic material. (English) Zbl 1423.74184
Summary: Fung’s theory of quasilinear viscoelasticity (QLV) was recently reappraised by the authors [“On nonlinear viscoelastic deformations: a reappraisal of Fung”s quasi-linear viscoelastic model”, Proc. R. Soc. A 479, No. 2166, Article ID 20140058 (2014; doi:10.1098/rspa.2014.0058)] in light of discussions in the literature of its apparent deficiencies. Due to the utility of the deformation of simple shear in a variety of applications, especially in experiment to deduce material properties, here QLV is employed to solve the problem of the simple shear of a nonlinear compressible quasilinear viscoelastic material. The effects of compressibility on the subsequent deformation and stress fields that result in this isochoric deformation are highlighted, and calculations of the dissipated energy associated with both a ‘ramp’ simple shear profile and oscillatory shear are given.

74D10 Nonlinear constitutive equations for materials with memory
74D05 Linear constitutive equations for materials with memory
74B20 Nonlinear elasticity
Full Text: DOI
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